erfa Package¶
Functions¶
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Decompose radians into degrees, arcminutes, arcseconds, fraction. |
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Decompose radians into hours, minutes, seconds, fraction. |
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Apply aberration to transform natural direction into proper direction. |
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Horizon to equatorial coordinates: transform azimuth and altitude to hour angle and declination. |
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Convert degrees, arcminutes, arcseconds to radians. |
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Normalize angle into the range 0 <= a < 2pi. |
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Normalize angle into the range -pi <= a < +pi. |
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For a geocentric observer, prepare star-independent astrometry parameters for transformations between ICRS and GCRS coordinates. |
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For a geocentric observer, prepare star-independent astrometry parameters for transformations between ICRS and GCRS coordinates. |
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For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and geocentric CIRS coordinates. |
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For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and geocentric CIRS coordinates. |
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For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and observed coordinates. |
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For a terrestrial observer, prepare star-independent astrometry parameters for transformations between ICRS and observed coordinates. |
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For an observer whose geocentric position and velocity are known, prepare star-independent astrometry parameters for transformations between ICRS and GCRS. |
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For an observer whose geocentric position and velocity are known, prepare star-independent astrometry parameters for transformations between ICRS and GCRS. |
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In the star-independent astrometry parameters, update only the Earth rotation angle, supplied by the caller explicitly. |
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In the star-independent astrometry parameters, update only the Earth rotation angle. |
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For a terrestrial observer, prepare star-independent astrometry parameters for transformations between CIRS and observed coordinates. |
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For a terrestrial observer, prepare star-independent astrometry parameters for transformations between CIRS and observed coordinates. |
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Transform a star’s ICRS catalog entry (epoch J2000.0) into ICRS astrometric place. |
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Quick transformation of a star’s ICRS catalog entry (epoch J2000.0) into ICRS astrometric place, given precomputed star-independent astrometry parameters. |
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Transform ICRS star data, epoch J2000.0, to CIRS. |
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Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed star-independent astrometry parameters. |
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Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed star-independent astrometry parameters plus a list of light- deflecting bodies. |
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Quick ICRS to CIRS transformation, given precomputed star- independent astrometry parameters, and assuming zero parallax and proper motion. |
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ICRS RA,Dec to observed place. |
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Transform star RA,Dec from geocentric CIRS to ICRS astrometric. |
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Quick CIRS RA,Dec to ICRS astrometric place, given the star- independent astrometry parameters. |
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Quick CIRS to ICRS astrometric place transformation, given the star- independent astrometry parameters plus a list of light-deflecting bodies. |
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CIRS RA,Dec to observed place. |
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Quick CIRS to observed place transformation. |
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Observed place at a groundbased site to to ICRS astrometric RA,Dec. |
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Observed place to CIRS. |
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Quick observed place to CIRS, given the star-independent astrometry parameters. |
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Frame bias components of IAU 2000 precession-nutation models; part of the Mathews-Herring-Buffett (MHB2000) nutation series, with additions. |
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Frame bias and precession, IAU 2000. |
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Frame bias and precession, IAU 2006. |
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Extract from the bias-precession-nutation matrix the X,Y coordinates of the Celestial Intermediate Pole. |
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Form the celestial-to-intermediate matrix for a given date using the IAU 2000A precession-nutation model. |
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Form the celestial-to-intermediate matrix for a given date using the IAU 2000B precession-nutation model. |
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Form the celestial-to-intermediate matrix for a given date using the IAU 2006 precession and IAU 2000A nutation models. |
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Form the celestial-to-intermediate matrix for a given date given the bias-precession-nutation matrix. |
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Form the celestial to intermediate-frame-of-date matrix for a given date when the CIP X,Y coordinates are known. |
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Form the celestial to intermediate-frame-of-date matrix given the CIP X,Y and the CIO locator s. |
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P-vector to spherical coordinates. |
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Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2000A precession-nutation model. |
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Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2000B precession-nutation model. |
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Form the celestial to terrestrial matrix given the date, the UT1 and the polar motion, using the IAU 2006/2000A precession-nutation model. |
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Assemble the celestial to terrestrial matrix from CIO-based components (the celestial-to-intermediate matrix, the Earth Rotation Angle and the polar motion matrix). |
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Assemble the celestial to terrestrial matrix from equinox-based components (the celestial-to-true matrix, the Greenwich Apparent Sidereal Time and the polar motion matrix). |
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Form the celestial to terrestrial matrix given the date, the UT1, the nutation and the polar motion. |
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Form the celestial to terrestrial matrix given the date, the UT1, the CIP coordinates and the polar motion. |
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Gregorian Calendar to Julian Date. |
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Copy a p-vector. |
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Copy a position/velocity vector. |
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Copy an r-matrix. |
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Format for output a 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds). |
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Decompose days to hours, minutes, seconds, fraction. |
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For a given UTC date, calculate Delta(AT) = TAI-UTC. |
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An approximation to TDB-TT, the difference between barycentric dynamical time and terrestrial time, for an observer on the Earth. |
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Encode date and time fields into 2-part Julian Date (or in the case of UTC a quasi-JD form that includes special provision for leap seconds). |
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Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using the IAU 2006 precession model. |
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ICRS equatorial to ecliptic rotation matrix, IAU 2006. |
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The equation of the equinoxes, compatible with IAU 2000 resolutions, given the nutation in longitude and the mean obliquity. |
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Equation of the equinoxes, compatible with IAU 2000 resolutions. |
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Equation of the equinoxes, compatible with IAU 2000 resolutions but using the truncated nutation model IAU 2000B. |
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Equation of the equinoxes, compatible with IAU 2000 resolutions and IAU 2006/2000A precession-nutation. |
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Equation of the equinoxes complementary terms, consistent with IAU 2000 resolutions. |
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Earth reference ellipsoids. |
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Equation of the origins, IAU 2006 precession and IAU 2000A nutation. |
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Equation of the origins, given the classical NPB matrix and the quantity s. |
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Julian Date to Besselian Epoch. |
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Besselian Epoch to Julian Date. |
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Julian Date to Julian Epoch. |
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Julian Epoch to Julian Date. |
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Earth position and velocity, heliocentric and barycentric, with respect to the Barycentric Celestial Reference System. |
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Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date) using IAU 2006 precession model. |
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Equation of the equinoxes, IAU 1994 model. |
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Earth rotation angle (IAU 2000 model). |
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Fundamental argument, IERS Conventions (2003): mean elongation of the Moon from the Sun. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Earth. |
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Fundamental argument, IERS Conventions (2003): mean longitude of the Moon minus mean longitude of the ascending node. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Jupiter. |
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Fundamental argument, IERS Conventions (2003): mean anomaly of the Moon. |
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Fundamental argument, IERS Conventions (2003): mean anomaly of the Sun. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Mars. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Mercury. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Neptune. |
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Fundamental argument, IERS Conventions (2003): mean longitude of the Moon’s ascending node. |
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Fundamental argument, IERS Conventions (2003): general accumulated precession in longitude. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Saturn. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Uranus. |
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Fundamental argument, IERS Conventions (2003): mean longitude of Venus. |
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Convert B1950.0 FK4 star catalog data to J2000.0 FK5. |
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Convert a B1950.0 FK4 star position to J2000.0 FK5, assuming zero proper motion in the FK5 system. |
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Convert J2000.0 FK5 star catalog data to B1950.0 FK4. |
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Transform FK5 (J2000.0) star data into the Hipparcos system. |
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Convert a J2000.0 FK5 star position to B1950.0 FK4, assuming zero proper motion in FK5 and parallax. |
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FK5 to Hipparcos rotation and spin. |
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Transform an FK5 (J2000.0) star position into the system of the Hipparcos catalogue, assuming zero Hipparcos proper motion. |
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Form rotation matrix given the Fukushima-Williams angles. |
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CIP X,Y given Fukushima-Williams bias-precession-nutation angles. |
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Transformation from Galactic Coordinates to ICRS. |
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Transform geocentric coordinates to geodetic using the specified reference ellipsoid. |
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Transform geocentric coordinates to geodetic for a reference ellipsoid of specified form. |
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Transform geodetic coordinates to geocentric using the specified reference ellipsoid. |
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Transform geodetic coordinates to geocentric for a reference ellipsoid of specified form. |
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Greenwich mean sidereal time (model consistent with IAU 2000 resolutions). |
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Greenwich mean sidereal time (consistent with IAU 2006 precession). |
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Universal Time to Greenwich mean sidereal time (IAU 1982 model). |
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Greenwich apparent sidereal time (consistent with IAU 2000 resolutions). |
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Greenwich apparent sidereal time (consistent with IAU 2000 resolutions but using the truncated nutation model IAU 2000B). |
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Greenwich apparent sidereal time, IAU 2006, given the NPB matrix. |
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Greenwich apparent sidereal time (consistent with IAU 2000 and 2006 resolutions). |
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Greenwich apparent sidereal time (consistent with IAU 1982/94 resolutions). |
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Transform Hipparcos star data into the FK5 (J2000.0) system. |
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Equatorial to horizon coordinates: transform hour angle and declination to azimuth and altitude. |
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Parallactic angle for a given hour angle and declination. |
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Transform a Hipparcos star position into FK5 J2000.0, assuming zero Hipparcos proper motion. |
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Transformation from ICRS to Galactic Coordinates. |
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Initialize an r-matrix to the identity matrix. |
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Julian Date to Gregorian year, month, day, and fraction of a day. |
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Julian Date to Gregorian Calendar, expressed in a form convenient for formatting messages: rounded to a specified precision. |
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Apply light deflection by a solar-system body, as part of transforming coordinate direction into natural direction. |
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For a star, apply light deflection by multiple solar-system bodies, as part of transforming coordinate direction into natural direction. |
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Deflection of starlight by the Sun. |
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Transformation from ecliptic coordinates (mean equinox and ecliptic of date) to ICRS RA,Dec, using a long-term precession model. |
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ICRS equatorial to ecliptic rotation matrix, long-term. |
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Transformation from ICRS equatorial coordinates to ecliptic coordinates (mean equinox and ecliptic of date) using a long-term precession model. |
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Long-term precession matrix. |
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Long-term precession matrix, including ICRS frame bias. |
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Long-term precession of the ecliptic. |
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Long-term precession of the equator. |
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Approximate geocentric position and velocity of the Moon. |
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Form the matrix of nutation for a given date, IAU 2000A model. |
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Form the matrix of nutation for a given date, IAU 2000B model. |
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Form the matrix of nutation for a given date, IAU 2006/2000A model. |
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Form the matrix of nutation. |
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Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation with free core nutation omitted). |
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Nutation, IAU 2000B model. |
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IAU 2000A nutation with adjustments to match the IAU 2006 precession. |
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Nutation, IAU 1980 model. |
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Form the matrix of nutation for a given date, IAU 1980 model. |
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Mean obliquity of the ecliptic, IAU 2006 precession model. |
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Mean obliquity of the ecliptic, IAU 1980 model. |
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Precession angles, IAU 2006, equinox based. |
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Extend a p-vector to a pv-vector by appending a zero velocity. |
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P-vector to spherical polar coordinates. |
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Position-angle from two p-vectors. |
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Position-angle from spherical coordinates. |
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This function forms three Euler angles which implement general precession from epoch J2000.0, using the IAU 2006 model. |
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p-vector inner (=scalar=dot) product. |
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Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation). |
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Approximate heliocentric position and velocity of a nominated major planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or Neptune (but not the Earth itself). |
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Modulus of p-vector. |
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Precession matrix (including frame bias) from GCRS to a specified date, IAU 2000 model. |
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Precession matrix (including frame bias) from GCRS to a specified date, IAU 2006 model. |
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Precession matrix from J2000.0 to a specified date, IAU 1976 model. |
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P-vector subtraction. |
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Proper motion and parallax. |
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Star proper motion: update star catalog data for space motion, with special handling to handle the zero parallax case. |
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Convert a p-vector into modulus and unit vector. |
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Precession-nutation, IAU 2000 model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly. |
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Precession-nutation, IAU 2000A model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly. |
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Precession-nutation, IAU 2000B model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly. |
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Precession-nutation, IAU 2006 model: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly. |
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Precession-nutation, IAU 2006/2000A models: a multi-purpose function, supporting classical (equinox-based) use directly and CIO-based use indirectly. |
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Form the matrix of precession-nutation for a given date (including frame bias), equinox based, IAU 2000A model. |
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Form the matrix of precession-nutation for a given date (including frame bias), equinox-based, IAU 2000B model. |
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Form the matrix of precession-nutation for a given date (including frame bias), equinox based, IAU 2006 precession and IAU 2000A nutation models. |
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Form the matrix of precession/nutation for a given date, IAU 1976 precession model, IAU 1980 nutation model. |
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Form the matrix of polar motion for a given date, IAU 2000. |
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P-vector addition. |
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P-vector plus scaled p-vector. |
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Precession-rate part of the IAU 2000 precession-nutation models (part of MHB2000). |
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IAU 1976 precession model. |
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Discard velocity component of a pv-vector. |
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Convert position/velocity from Cartesian to spherical coordinates. |
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Inner (=scalar=dot) product of two pv-vectors. |
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Modulus of pv-vector. |
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Subtract one pv-vector from another. |
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Add one pv-vector to another. |
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Convert star position+velocity vector to catalog coordinates. |
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Position and velocity of a terrestrial observing station. |
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Update a pv-vector. |
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Update a pv-vector, discarding the velocity component. |
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Outer (=vector=cross) product of two pv-vectors. |
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p-vector outer (=vector=cross) product. |
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Determine the constants A and B in the atmospheric refraction model dZ = A tan Z + B tan^3 Z. |
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Express an r-matrix as an r-vector. |
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Form the r-matrix corresponding to a given r-vector. |
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Rotate an r-matrix about the x-axis. |
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Multiply a p-vector by an r-matrix. |
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Multiply a pv-vector by an r-matrix. |
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Multiply two r-matrices. |
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Rotate an r-matrix about the y-axis. |
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Rotate an r-matrix about the z-axis. |
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The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, given the CIP’s X,Y coordinates. |
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The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2000A precession-nutation model. |
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The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2000B precession-nutation model. |
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The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, given the CIP’s X,Y coordinates. |
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The CIO locator s, positioning the Celestial Intermediate Origin on the equator of the Celestial Intermediate Pole, using the IAU 2006 precession and IAU 2000A nutation models. |
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Convert spherical coordinates to Cartesian. |
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Convert spherical polar coordinates to p-vector. |
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Convert position/velocity from spherical to Cartesian coordinates. |
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Multiply a pv-vector by two scalars. |
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Angular separation between two p-vectors. |
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Angular separation between two sets of spherical coordinates. |
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The TIO locator s’, positioning the Terrestrial Intermediate Origin on the equator of the Celestial Intermediate Pole. |
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Star proper motion: update star catalog data for space motion. |
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Convert star catalog coordinates to position+velocity vector. |
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Multiply a p-vector by a scalar. |
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Multiply a pv-vector by a scalar. |
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Time scale transformation: International Atomic Time, TAI, to Terrestrial Time, TT. |
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Time scale transformation: International Atomic Time, TAI, to Universal Time, UT1. |
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Time scale transformation: International Atomic Time, TAI, to Coordinated Universal Time, UTC. |
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Time scale transformation: Barycentric Coordinate Time, TCB, to Barycentric Dynamical Time, TDB. |
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Time scale transformation: Geocentric Coordinate Time, TCG, to Terrestrial Time, TT. |
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Time scale transformation: Barycentric Dynamical Time, TDB, to Barycentric Coordinate Time, TCB. |
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Time scale transformation: Barycentric Dynamical Time, TDB, to Terrestrial Time, TT. |
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Convert hours, minutes, seconds to radians. |
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Convert hours, minutes, seconds to days. |
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In the tangent plane projection, given the rectangular coordinates of a star and its spherical coordinates, determine the spherical coordinates of the tangent point. |
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In the tangent plane projection, given the rectangular coordinates of a star and its direction cosines, determine the direction cosines of the tangent point. |
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In the tangent plane projection, given the star’s rectangular coordinates and the spherical coordinates of the tangent point, solve for the spherical coordinates of the star. |
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In the tangent plane projection, given the star’s rectangular coordinates and the direction cosines of the tangent point, solve for the direction cosines of the star. |
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In the tangent plane projection, given celestial spherical coordinates for a star and the tangent point, solve for the star’s rectangular coordinates in the tangent plane. |
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In the tangent plane projection, given celestial direction cosines for a star and the tangent point, solve for the star’s rectangular coordinates in the tangent plane. |
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Transpose an r-matrix. |
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Multiply a p-vector by the transpose of an r-matrix. |
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Multiply a pv-vector by the transpose of an r-matrix. |
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Time scale transformation: Terrestrial Time, TT, to International Atomic Time, TAI. |
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Time scale transformation: Terrestrial Time, TT, to Geocentric Coordinate Time, TCG. |
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Time scale transformation: Terrestrial Time, TT, to Barycentric Dynamical Time, TDB. |
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Time scale transformation: Terrestrial Time, TT, to Universal Time, UT1. |
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Time scale transformation: Universal Time, UT1, to International Atomic Time, TAI. |
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Time scale transformation: Universal Time, UT1, to Terrestrial Time, TT. |
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Time scale transformation: Universal Time, UT1, to Coordinated Universal Time, UTC. |
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Time scale transformation: Coordinated Universal Time, UTC, to International Atomic Time, TAI. |
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Time scale transformation: Coordinated Universal Time, UTC, to Universal Time, UT1. |
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X,Y coordinates of celestial intermediate pole from series based on IAU 2006 precession and IAU 2000A nutation. |
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For a given TT date, compute the X,Y coordinates of the Celestial Intermediate Pole and the CIO locator s, using the IAU 2000A precession-nutation model. |
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For a given TT date, compute the X,Y coordinates of the Celestial Intermediate Pole and the CIO locator s, using the IAU 2000B precession-nutation model. |
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For a given TT date, compute the X,Y coordinates of the Celestial Intermediate Pole and the CIO locator s, using the IAU 2006 precession and IAU 2000A nutation models. |
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Zero a p-vector. |
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Zero a pv-vector. |
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Initialize an r-matrix to the null matrix. |
Classes¶
A class for errors triggered by ERFA functions (status codes < 0) |
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A class for warnings triggered by ERFA functions (status codes > 0) |
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Leap second management. |